Concepts of Elasticity of Demand
Topic Eight

### Price Elasticity of Demand (|Ed|)

Elasticity is a measure of how much the quantity demanded will be affected by a change in price or income or change in price of related goods. There are three main types of elasticities: price elasticity of demand, income elasticity of demand and cross elasticity of demand.

When the price of a good falls, the quantity demanded of the good will normally rise.

Price elasticity of demand measures the responsiveness of a change in quantity demanded for a good or service to a change in its price. Mathematically, the price elasticity of demand is the ratio of the relative (or percentage) change in quantity demanded to the relative (or percentage) change in price.

For example:

Price Elasticity of Demand = %△ QD/ %△P x P/QD

P is the original price and Q the original quantity)

If price of a product falls from \$10 to \$5 and quantity demanded increases from 20 to 40, then the price elasticity is calculated as

20 / -\$5 x \$10/20 = - 4 x 0.5 = - 2

This means that this product is highly elastic because it is greater than 1. As a result, small changes in prices will lead to large changes in quantity demanded. Since the demand curve is downward sloping, the price elasticity will always have a negative sign. To interpret the calculation, simply use the positive or absolute value obtained. As in the example above the -2 must be interpreted as +2. As a general rule therefore, when the price elasticity of demand is greater than one, we say that demand is price elastic and when it is less than one, we say that demand is price inelastic.

### Degrees of Elasticity

The demand curve in graph (a) shows the case when demand is inelastic – in this case the demand curve is steep; therefore, the steeper is the demand curve, the more inelastic will be demand. The demand curve in graph (b) is for the case of the demand curve that is elastic. Therefore, the more gently sloping is the demand curve, the more elastic will be demand.

Graph (c) is for the case for a perfectly elasticity curve. In such a case, the market is extremely elastic and price changes will have a huge impact on demand. Graph (d) shows the case of a perfectly inelastic demand curve. In such a case, changes in price will have no impact or effect on quantity demanded.

There are times when elasticity can also be unitary elastic as can be seen in graph (e). In such a case, a change in price will result in quantity demanded being changed by the exact amount as the change in price.

### Elasticity and Total Revenue

Price elasticity is important in that knowledge of it gives the seller an indication of how to change prices in order to maximize profits. When the price elasticity of demand for a good is inelastic, the percentage change in quantity is smaller than that in price. Hence, when the price is raised, the total revenue of producers rises, and vice versa. When the price elasticity of demand for a good is elastic, the percentage change in quantity is greater than that of price. Hence, when the price is raised, the total revenue of producers falls, and vice versa. When the price elasticity of demand for a good is unit elastic, the percentage change in quantity demanded is equal to that of the change in price. Hence, when the price is raised, the total revenue remains unchanged.

### Determinants of Price Elasticity of Demand

The following is a summary of the factors that influence the price elasticity of demand:

• Number of substitutes – If a product can be easily substituted, its demand is elastic. If a product cannot be substituted easily, its demand is inelastic.
• Necessity vs Luxury – Demand for necessities is usually inelastic because there are usually very few substitutes for necessities such as food and medical products.
• The Percentage of Income Spent on the Good – The larger the percentage of income spent on a good, the more elastic is its demand. A change in these products' price will be highly noticeable as they affect consumers' budget with a bigger magnitude.
• Time lag – The longer the time after the price change, the more elastic will be the demand. This is so because consumers are given more time to carry out their actions.
• The Definition of a Good or Service – if a good is broadly defined, i.e. the demand for petrol or meat, demand is often inelastic. However, specific brands of petrol or meat are likely to be more elastic following a price change.

### Income Elasticity of Demand

Income elasticity is defined as the change in demand when income changes. To measure this response, we have the income elasticity of demand,

If the income elasticity is positive, we say that the good is a normal good which means that the demand for such a good rises when income rises. If the income elasticity is negative, we say that the good is an inferior good meaning that as income rises, the demand for this good will fall.

We might even observe that the income elasticity of demand may be less than one for some goods. Necessities have an income elasticity of demand of between 0 and +1. Demand rises with income, but less than proportionately. Often this is because we have a limited need to consume additional quantities of necessary goods as our real living standards rise.

Luxuries on the other hand are said to have an income elasticity of demand > +1. In this case, demand rises more than proportionate to a change in income. Luxuries are items we can manage to do without during periods of below average income and falling consumer confidence.

### Cross Elasticity of Demand

Sometimes the price of one good may cause a change in demand for another good. A measure of this responsiveness is referred to as cross elasticity. For example, an increase in the price of chicken may increase the demand for beef. Cross-elasticity of demand is calculated as:

As an example, suppose the price of chicken goes up by 10 percent and as a result the quantity demanded of beef increases by 4 percent (assuming with no change in the price of beef or anything else that would influence the demand for beef). Then the cross-elasticity of demand for beef, with respect to the price of chicken, is 4/10 = 0.4.

If the cross elasticity is positive, it means that an increase in the price of one good will increase the demand for the other good. When we observe a positive cross-elasticity, we say that the two goods are substitutes.

If the cross-elasticity of demand is negative, then an increase in the price of one good decreases the demand for the other. For example, if the price of cars increases then we may expect that the demand for petrol will decrease. In this case, we say that these two goods are complements.

### Price Elasticity of Supply

Price elasticity of supply measures the degree of sensitivity of production to a change in price. It is calculated as:

Es = % change in Quantity Supplied Qs /% change in Price

Example:

If the price of Product A increased by 40% and the quantity supplied increases by 20%, then the price elasticity of the supply of Product A is:

Es = percentage change in Qs / percentage change in Price = (20)/ (40) = 0.5

The price elasticity coefficient will always be positive because there is a positive relationship between price and quantity supplied. When price increases, quantity supplied increases and when price declines, quantity supplied falls.